Show the conjecture is false by finding a counterexample: The absolute value of the sum of two numbers is the sum of their absolute values

Q: You are given a real number N. How should you write it as a sum of two real numbers so that their…

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Q: (b) With domain of discourse as the real numbers, determine if the following state- ment is true or…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

Q: Solve the given inequality and write the solution in interval notation: -7z < 56 O [-8, )

A: Here we have given an inequality. -7x &lt; 56 Now on dividing both sides of the inequality by 7 we…

Q: How would you convince someone that (x - 4)/(4 - x) = -1 for all real numbers except 4?

A: here given rational equation such that x-44-x=-1where x≠4

Q: Which x satisfies both Ix - 31 &lt; 2 and Ix - 51 &lt; 1?

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Q: true or False For all number x, then |x| > 0.

A: For all number x then |x|&gt;0

Q: the arithmetic mean of two unequal positive real number 'a' and 'b'; (a> b). be twice as great as…

A: Given : Arithmetic mean = 2* geometric mean We have to prove the mentioned condition.

Q: Write the expression  |x − 5| + |x − 7|  without the absolute value symbols if x is in the given…

A: Consider the given expression as According to definition of absolute value of function,

Q: 1 plus 1 is equals to? and why?

A: Given: Determine and 1 plus 1 equals and its reason.

Q: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

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Q: express in interval notation: x2 - x is less than or equal to 6

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Q: Q 1. (a) Let R, the set of real numbers, be the universal set, A = (-3,6], B = [4, 8) and C = [2,…

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Q: Unit 4 Performance Task Name: Zo 4.3.3 Justify the volume formula for a solid sphere. Learning…

A: GIVEN: STAR'S GENERATION OF POWER Pinterior​=cm33×10−7watts​Psurface​=cm26000watts​ 1.Given:…

Q: the real number line which equals 1 Qs-, n=1 " + ] ကျေ 18+

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Q: ) Recall that r > 0 for every positive real number r. Prove that if a and b are positive real…

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Q: What does the set of real numbers consist of?

A: To discuss about real number

Q: The set of real numbers in interval notation is represented by

A: The set of real numbers in interval notation is represented by ℝ=-∞,∞.  Interval: An interval  a,b…

Q: why is the absolute value of r less than 1

A: A series is said to be convergent, if the sum of the terms present in the series is a finite number.…

Q: Determine the set of real numbers: {TER: T=1 ≥ 4, a #2} by considering the two cases: z-2> 0 and…

A: The details are nicely explained in step 2.

Q: What is the absolute value of a number a and what is it denoted by?

A: Absolute value:   The absolute value of a real number “a” is denoted by |a| (mod a) and it is the…